I just stumbled across a new phrase 无消息。
This is the first time I've encountered 无.
How it is used, and how it is different from 没有，as in 没有消息？
It is hard to give a rule on using 无 vs 没有， even they mean the same.
Only 无 is used:
无所谓 （We don't say 没有所谓, but some people say 没所谓）
无线电 （We don't say 没有线电）
无论如何 （We don't say 没有论如何）
无性繁殖 （We don't say 没有性繁殖）
Only 没有 is used:
我没有钱 （We don't say 我无钱）
你没有失败 （We don't say 你无失败）
Both can be used:
没有 消息就是好消息。 or 无 消息就是好消息。
没有 人能猜出这个谜语。 or 无 人能猜出这个谜语。
I think there are still some clues on using 无 vs 没有.
无 is more like 'non-' or "un-"in English, and 无 is used in some Idioms or fixed phrases, like 无所谓, 无论如何, 无土栽培, 无独有偶, 无恶不作 etc. In those words, we don't use 没有.
When 没有 is used for "not" in English to negate something, 没有 can NOT be replaced with 无. For example, 他没有做完作业. We don't say 他无做完作业.
When 没有 is used for "without" in English, it can be replaced with 无. But I am not sure if it is always true. For example, 无人喝彩. We can say 没有人喝彩. But if used as a tile of a book, a story, or a movie, 无人喝彩 is better, but using 没有人喝彩 is also ok.
沒有 is the common word for "no/none" used in conversation.
無 is a character that is used in words and set phrases, and cannot be used by itself.
Put it in simple way,
无 means lack of (noun objects), i.e. 无语（lack of speech-> speechless）
没 means lack of (an action), i.e. 没有（lack of having-> don't have）
So it would be better to compare 无 and 没
In general, the meaning of "无" is "沒有".
"沒有", can serve as a component of a sentence. I think in technical terms, you can say it can serve as predicates in sentences.
So in this sense, "没有" is more like "There be no" in a sentence. For example:
There are no people here.
Technically, "无" is more similar to "no","non-", "-less", "-free" in English when constructing a phrase or word. It sounds more formal, and it normally (in modern Chinese) cannot be used as predicates in sentences.
Unpopulated (human-free) zone
without information (as the name of a status)
He wanted to update the application, but the program showed "no updates available".
basically, same meaning, but 没有 for modern people, 无 for people from hundred years ago....
In my opinion, the most significant difference is that 无 can be used as a bound morpheme, but 沒有 is always a word.
For example 无形资产 can never be "沒有形资产". It is 无形的, and it 沒有实物形态.